Gwede Mantashe made the comments after deputy Finance Minister Mcebesi Jonas alleged the Gupta family had offered him a government promotion.
The family has denied the allegation.
Main opposition leader Mmusi Maimane was thrown out of parliament during a rowdy session over the controversy.
Mr Mantashe is the third most powerful person in the governing African National Congress (ANC), and his remarks suggest Mr Zuma may be losing the confidence of influential members of the party, correspondents say.
Mr Zuma`s presidency has been marred by allegations of corruption, cronyism and incompetence, amid a worsening economic situation.
South Africa Gupta row: ANC`s Mantashe warns of `mafia state`
18 March 2016
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South Africa risks turning into a "mafia state", a senior governing party official has warned, as pressure grows on President Jacob Zuma over his links with a wealthy family.
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